Chemical Formulas and Representations Summary

Molecular representations and models

• Molecular formula: uses chemical symbols with subscripts to show the types and numbers of atoms in a molecule; a subscript is used only when more than one atom of a given type is present. Used as an abbreviation for the compound’s name. Example: $ext{CH}_4$ for methane.
• Structural formula: conveys the same atom types and counts as the molecular formula but also shows how atoms are connected; lines indicate bonds.
• Ball-and-stick model: shows geometric arrangement of atoms; not to scale.
• Space-filling model: shows relative sizes of atoms.
• Methane representations: (a) molecular formula, (b) structural formula, (c) ball-and-stick model, (d) space-filling model.

Subscripts and formulas: meanings and differences

• A subscript after a symbol (e.g., $ext{H}_2$) counts atoms in a molecule; a coefficient (e.g., 2H) indicates multiple atoms or entities.
• Distinction:
  • $ext{H}_2$: a diatomic molecule of hydrogen (two hydrogen atoms bonded together).
  • $2 ext{H}$: two separate hydrogen atoms (not bonded as a unit).
  • $2 ext{H}_2$: two molecules of diatomic hydrogen.
• This shows that symbols like H, H2, 2H, and 2H2 represent different entities.

Empirical vs molecular formulas

• Empirical formula: the simplest whole-number ratio of the types of atoms in a compound.
• Molecular formula: shows the actual number of each type of atom in a molecule.
• Relationship: the molecular formula is always a whole-number multiple of the empirical formula.
• Example: titanium dioxide has empirical formula $ext{TiO}_2$ (ratio 1 Ti : 2 O).

From empirical to molecular formulas and back

• In many cases, the molecular formula is determined experimentally from both empirical formula and molecular mass.
• If a compound’s empirical formula is known, multiplying by an integer gives the molecular formula.

Benzene: a key example

• Benzene molecular formula: $ext{C}<em>6 ext{H}</em>6$
• Its empirical formula: $ext{CH}$ (for every carbon atom there is one hydrogen).
• Benzene can be represented as structural, ball-and-stick, or space-filling models.

Acetic acid: a detailed example

• Molecular formula: $ext{C}<em>2 ext{H}</em>4 ext{O}_2$.
• Empirical formula: $ext{CH}_2 ext{O}$.
• Atom ratio in empirical formula: $2:4:2$ for $ext{C:H:O}$.
• Simplified ratio: dividing by the lowest common denominator 2 gives $1:2:1$, so empirical formula is $ext{CH}_2 ext{O}.$
• Acetic acid can be depicted as structural, ball-and-stick, or space-filling models.

Quick takeaways

• Different representations highlight different aspects: composition (molecular formula), connectivity (structural formula), and geometry (ball-and-stick, space-filling).
• Subscripts vs coefficients convey fundamentally different ideas; be careful to distinguish them.
• Empirical formulas give the simplest atom ratio; molecular formulas give the actual atoms in a molecule; the former scales to the latter by a whole-number factor.
• Many elements exist as diatomic molecules (e.g., $ext{H}<em>2, ext{O}</em>2, ext{N}<em>2, ext{F}</em>2, ext{Cl}<em>2, ext{Br}</em>2, ext{I}<em>2$); sulfur commonly forms $ext{S}</em>8$ rings.